Umm, so on that bipolar, where does the sun go every day? literally over the tops of the poles?
Or on some goofy figure 8 where it's sunny twice a day between the poles?
And dual earth, hmm. I think there are still distortion issues.
If we're going to have two earths, maybe we could have three, or four, or how about a Multifaceted-Spheroid?

I think we will find that the closer our earths approximate the globe, the less stretch error we will have.
As to Sandokahn's true flat map, umm, if I'm not mistaken, Australia is rather long there too. I'm so glad Australians like to drive a hundred miles an hour (160km/h) and fly supersonic all the time!
Because that's the only way they can get from one end of Australia to the other on most of these maps.
And I don't even want to try to bust up my brain trying to figure out how you get from one half of the dual earth to the other
Like you said, they only make things harder on themselves trying to solve problems.